Polycrystalline Model Research Articles

An Improvement of Multiaxial Ratchetting Modeling Via Yield Surface Distortion

Many theoretical studies have been made to describe multiaxial ratchetting and most of them have been concentrated on the location of the yield domain, not on its shape. In this paper, we introduce nonlinear kinematic constitutive equations consistent with ratchetting modeling into the distortional model of subsequent yield surfaces proposed by Kurtyka, T., and Zyczkowski, M. We use an efficient polycrystalline model to simulate complex tests including yield surface detections in order to get some reference predictions to use in the development of the constitutive laws introduced into the distortional model. The distortional model is thus qualitatively identified with the polycrystalline model and then quantitatively identified with the experimental results on a type 316L stainless steel. It gives promising results.

A study of twinning in zirconium using neutron diffraction and polycrystalline modeling

An experimental study using neutron diffraction quantified the evolution of twinning in pure clockrolled zirconium that was subsequently deformed under uniaxial compression. The clock rolling introduced an initial texture of approximately 5 times random, and the compression specimens were cut with their loading axes nearly parallel to the predominant c-axes direction. Seven specimens deformed to strains between −2 and −17 pct and an undeformed specimen (0 pct strain) were examined. The deformation was performed at an applied strain rate of 0.001/s at 77 K. Twin volume fractions were estimated from diffraction data. Changes in texture and twin volume fractions were compared to predictions from a visco-plastic self-consistent (VPSC) polycrystal model, which described both slip and twinning. This work demonstrates the feasibility of using neutron diffraction to track the evolution of twinning. These results help benchmark the polycrystalline model, validate the description of twinning, and potentially lead to a better understanding of its role in hardening.

A study of twinning in zirconium using neutron diffraction and polycrystalline modeling

A study of twinning in zirconium using neutron diffraction and polycrystalline modeling

A polycrystalline model for stress-strain behaviour of tantalum at 300 K

A polycrystalline model is proposed to model the large plastic deformation and texture evolutions in tantalum over a wide range of strain rates at room temperature. The mechanical behaviour is discussed in terms of back and effective stresses with the help of qualitative and quantitative TEM observations. Using these observations, an elasto-visco-plastic formulation for b.c.c. crystals is developed in the thermal activation framework.

Texture dependent plastic behavior of Zr 702 at large strain

Three polycrystalline samples of Zr702α are deformed at room temperature under channel die compression until about 40% strain. Samples are oriented differently in the die with respect to their texture, so that the influence of the initial texture on the stress–strain response, the activated deformation systems, and the subsequent texture evolution can be assessed. Experimental results are interpreted by using a viscoplastic self-consistent (VPSC) polycrystalline model in which a saturating anisotropic intracrystalline hardening law is introduced. It is shown that the orientation dependence of the activated slip systems strongly depends on the texture of the polycrystal. The main effect of intracrystalline hardening is found to be a redistribution of slip from the primary to the secondary systems, but in a moderate way such that it does not affect significantly the development of texture. A simple analysis shows that the increasing activity of the secondary slip systems can be assessed directly from the macroscopic stress–strain curves.

Determination of Constitutive Equation Parameter Using Finite Element Polycrystalline Model.

A plastic constitutive theory incorporating the directional dependence of the plastic strain increment dep on the stress increment dσ' was proposed by Goya and Ito. The expression was given in terms of two transition parameters μ(α) and β(α) which denote the magnitude and the direction angle of the plastic increment, where α denotes the direction angle of the stress increment measured from a particular direction nN, named direction, in which the direction of the stress increment coincide with that of the plastic strain increment. In this report, a computer code for a finite element polycrystalline model is used for the numerical investigation of the variation of the two constitutive parameters μ(α) and β(α) of anisotropic plastic materials. The results show that the approximate functions for the two transition parameters are numerically determined and the direction dependence rule can be naturally extended for anisotropic plastic materials. It is also suggested that several quadratic functions used for classical plastic potential may be introduced for the natural direction potential whose normal is identical to the natural direction.

Texture development of wire drawn Cu–Fe composites

Polycrystalline models have shown to be powerful tools for prediction of texture developments which is mainly used to analyze textures of different types of materials. When more than one phase is present, it is necessary to take into account their interaction because of their elastic and plastic co-deformation. We have considered wire drawn Cu–Fe samples with a well-defined microstructural state and relatively soft deformation steps of 0.25 equivalent Von Mises strains (VM) up to 3.0 VM. Both phases show typical FCC and BCC wire textures with a texture sharpness depending on the strain. Texture simulations using a 2-site viscoplastic self-consistent model as a constitutive equation in a fully 3D finite element code give results in good qualitative agreement with the experimental ones.

932 軸対称多結晶体のねじり変形挙動のシミュレーション

It is well-known that the torsional deformation behavior of polycrystalline materials is significantlly depending on the characteristic length such as grain size and diameter of wires. In order to reproduce the torsional deformation behavior that depends on these characteristic length, we develop a polycrystalline model that can be used for the axisymmetric torsion problem. Through the finite element simulation, we clarified the effect of grain size and diameter of wires on the deformation behavior of polycrystalline materials.

Rate-independent crystalline and polycrystalline plasticity, application to FCC materials

This paper deals with the simulation of the mechanical response and texture evolution of cubic crystals and polycrystals for a rate-independent elastic–plastic constitutive law. No viscous effects are considered. An algorithm is introduced to treat the difficult case of multi-surface plasticity. This algorithm allows the computation of the mechanical response of a single crystal. The corresponding yield surface is made of the intersection of several hyper-planes in the stress space. The problem of the multiplicity of the slip systems is solved thanks to a pseudo-inversion method. Self and latent hardening are taken into account. In order to compute the response of a polycrystal, a Taylor homogenization scheme is used. The stress–strain response of single crystals and polycrystals is computed for various loading cases. The texture evolution predicted for compression, plane strain compression and simple shear are compared with the results given by a visco-plastic polycrystalline model.

Simulation of the orientation dependence of stored energy during rolling deformation of low carbon steels

In order to furnish some input data to Monte Carlo codes developed for the simulation of static recrystallization in low carbon steels, two polycrystalline models are used in conjunction with four different hardening laws to estimate numerically the stored energy within individual grains, which is due to the increase in dislocation density during rolling. Three quantities are calculated as a function of final orientation, which are believed to be good estimates of this energy: these are the average dislocation density (linked to the square of an average reference shear stress), the total plastic work and the final plastic work rate. It is thus found that the three selected parameters present the same variation trends for a given model, whatever the hardening law. However, the Taylor and VPSC models lead to opposite conclusions: at the end of the simulated rolling process, the (respectively ) orientations are the hardest (respectively softest) with the Taylor model and the softest (respectively hardest) with the VPSC one; thus, the present data cannot be used in the present state to perform recrystallization simulations but may be used to validate the different polycrystalline models, since they are more sensitive to the interaction law than the texture evolution or macroscopic response.

Piezoresistive effect in p-type polycrystalline diamond films

The piezoresistive effect of boron-doped polycrystalline diamond films was analyzed and discussed by the famous M-S polycrystalline model. It is found that the valence bands splitting-off and the grain-boundary scattering are the main factors responsible for the piezoresistive effect in the p-type polycrystalline diamond films. The gauge-factor calculation formula including the effect of both background scattering and grain-boundary scattering were obtained, and the calculation results are in accordance with the experimental results.

An elastic–plastic constitutive law for the description of uniaxial and multiaxial ratchetting

Abstract An elastic–plastic constitutive model is proposed to describe 1-D and 2-D ratchetting. The model is also able to give correct results for 2-D ratchetting when only uniaxial identification is used, while no special threshold or parameter is used for the case of non-proportional loading. The original feature of this model consist in the introduction of a ratchetting stress (material characteristic) along with the maximal stress supported in the history of loading and the plastic strain at the last unloading. In this paper uniaxial and 3-D formulations have been described based on a numerical implementation in the software Code_Aster. Uniaxial and also multiaxial identifications have been used. Simulations have been realized for proportional and non-proportional homogeneous cases, as well as for structures under anisothermal thermomechanical loading. The results of a benchmark on a structure, comparing experiment, simulations by this model and some other phenomenological models, and a polycrystalline model are presented. An analysis of error margin due to the choice of Mises criterion is exposed.

Finite Element Simulations of the Deformation of BCC Aggregates Using a Crystal Plasticity Model - Local Orientation Effects

AbstractOne has simulated by a finite element computation, the tensile plastic deformation of bcc aggregates with the same initial crystallographic texture but a different spatial distribution of orientations. The computations show fairly large differences between the simulations in terms of axial strain fields: one aggregate presents an homogeneous field, while another one localizes the strain in a narrow band. This “macroscopic effect” is then analyzed at the smaller scale of the crystallite by comparing local re-orientations, glide activity and stress levels. The influence of neighboring grains and of the “local”texture is thus shown. This is an effect that polycrystalline models (Taylor or self-consistent models) cannot account for.

Crystal plasticity: micro-shear banding in polycrystals using voronoi tessellation

Abstract A Taylor-type polycrystalline model, together with a new time-integration scheme, has been developed and implemented into a finite element program to simulate the development of micro shear bands in single- and polycrystal of fcc metals. In order to take numerical advantages associated with a symmetric stiffness matrix, the stiffness tensor which arises from the crystal plasticity formulation is symmetrized and the constitutive equation is rearranged accordingly. It is shown that this approach yields significant reduction in computational time without affecting the numerical results. The mesoscopic behavior of polycrystals is analyzed using Voronoi tessellation in which the randomness of the microstructure is generated using a Delaunay network from which a random distribution of grains is generated. The use of 3-node and 4-node elements to analyze the phenomena of shear banding in polycrystals is investigated. It is shown that the use of triangular elements to capture the shear banding phenomenon in polycrystals depends critically on the mesh design, since the resulting mesh is highly nonuniform. However, this problem is resolved by using a 4-node element with reduced integration, illustrating the formation of micro shear bands in a polycrystal using a nonuniform mesh.

Grain orientation effects in Zr702 α polycrystalline samples deformed in channel die compression at room temperature

Deformation mechanisms are determined in five zirconium polycrystalline samples deformed by channel die compression at room temperature (T1–T5 textures). Slip systems are characterized by a slip trace analysis and twinning systems by a misorientation calculation between twinned and non-twinned parts of the grains, from Electron Back Scattering Diffraction (EBSD) measurements. The analysis is completed by the measurement of crystallographic texture evolutions and the examination of the stress–strain curves. Prismatic glide and {10 12} twinning are identified as primary deformation modes and first-order pyramidal slip {10 11} and basal slip as secondary slip modes. The experimental study is completed by a numerical approach using polycrystalline models which is consistent with the experimental observations.

A micromechanical model for dual-phase superplastic materials

A micromechanics based polycrystalline model was previously developed from the grain level to describe the flow behavior of pseudo-single phase superplastic materials. In this work the previous model is extended to characterize the superplastic behavior of two-phase materials. This is achieved by incorporating the elastic and inelastic properties of the individual phases at the level of slip systems, and invoking self consistent relation to account for stress redistribution. The model is applied to two conventional dual-phase superplastic materials: Ti–6Al–4V and Zn–22Al. The material constants, including the threshold stresses ( σ *) used in the model are evaluated from one set of experimental stress–strain rate data. The model is then used to predict the flow stress as a function of temperature and grain size and strain rate sensitivity ( m) for a wide range of strain rates. The micro level threshold stress ( σ *) introduced at the level of slip planes in the diffusional equations manifests itself as the experimentally observed threshold stress at the macro level, and was found to be a strong function of temperature. The contribution of diffusion and dislocation in the accommodation process is computed. Diffusion dominates at lower strain-rate region while dislocation plays a more significant role at higher strain-rate ranges.

Size and temperature dependence of electrical resistance and thermoelectric power of Bi2Te2Se1 thin films

Thin films of Bi2Te2Se1 of various thicknesses have been deposited on clean glass plates using the flash evaporation technique. Electrical resistance and thermoelectric power measurements have been carried out on these films in the temperature range 300–485 K. The thickness dependences of electrical resistivity and thermoelectric power of the films have been analyzed using the effective mean-free path model. The thickness dependence of activation energy of the films is explained by Seto’s polycrystalline model. Various material parameters such as mean-free path and Fermi energy have been calculated from the analysis of experimental data. The thermoelectric power factor of the films has been calculated using the measured electrical resistivity and thermoelectric power values.

Computational prediction of the localized necking in sheet forming based on microstructural material aspects

The paper deals with the influence of microstructural material aspects on the localized necking in sheet metal forming. The approach developed accounts for various microstructural material aspects as crystallographic slip, work hardening at microstructural level and lattice rotation which induces the texture evolution. The analyses are performed using the linear stability analysis combined with a polycrystalline model to build Forming Limit Diagrams and to study their evolution with the initial and induced anisotropy.

A Viscoplastic Simulation of Texture Evolution during Extrusion of an Aluminium Alloy

Numerical simulations of texture development have been carried out for hot plane strain extrusion of an aluminium alloy using both finite element calculations and a polycrystal plasticity model. The latter is based on the Taylor localisation hypothesis (relaxed constraints) and a viscoplastic constitutive law. We have considered the {111} slip systems and the {100}, {110} and {112} non-octahedral systems. The finite element code first simulates the local extrusion strain paths of the material flow through the die. Secondly, for the different deformation paths between the centre section and the surface the polycrystalline model is used to calculate the local deformation texture evolution. The results are compared with experimentally measured deformation textures at different depths of an extruded bar of a 6082 aluminium alloy. Near the centre section both the numerical simulations and the experimental textures are in good agreement, with typical β-fibre hot rolling texture components as a consequence of the essentially plane strain compression deformation mode. Texture simulations using the non-compact slip systems give significantly better agreement than for slip restricted to the {111} planes. However, very near the surface where there is a very high shear component, none of the models gives good quantitative predictions although there is a reasonable qualitative agreement assuming non-octahedral slip.

F.E. computation of a triaxial specimen using a polycrystalline model

The crystallographic approach provides an improved framework with respect to the classical macroscopic models to predict the stress-strain behavior of polycrystalline material. The model consists in a set of equations to represent the phase behavior, and a concentration rule. The present paper shows a numerical implementation of such a model, written in the framework of viscoplasticity with a threshold, in a parallel version of the F.E. code ZéBuLoN. Heavy computations can then be made. The system is used to simulate the mechanical response of a biaxial specimen developed at Laboratoire de Mécanique et Technologie de Cachan. This type of specimen is specially designed to support three-dimensional non-proportional loading paths, which are badly represented by classical models. The response obtained with the polycrystalline model is shown, and compared with the experimental data at the global scale. Local information concerning the stress and strain heterogeneity and the slip system activity are also available from the computation.